# CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics

arXiv: https://arxiv.org/abs/2310.05963 · HTML: https://mlsanity.com/paper/2310.05963/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 55 references that are in the map.
- First posted on arXiv 13 Sep 2023.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [MetNet: A Neural Weather Model for Precipitation Forecasting](https://mlsanity.com/paper/2003.12140/) (2020)
- [PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs](https://mlsanity.com/paper/2106.14103/) (2021)
- [CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method](https://mlsanity.com/paper/2110.15832/) (2021)
- [Improved architectures and training algorithms for deep operator networks](https://mlsanity.com/paper/2110.01654/) (2021)
- [LNO: Laplace Neural Operator for Solving Differential Equations](https://mlsanity.com/paper/2303.10528/) (2023)
- [Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology](https://mlsanity.com/paper/2211.08939/) (2022)
- [SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability](https://mlsanity.com/paper/2204.12670/) (2022)
- [Koopman neural operator as a mesh-free solver of non-linear partial differential equations](https://mlsanity.com/paper/2301.10022/) (2023)
- [Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations](https://mlsanity.com/paper/2212.04663/) (2022)
- [Enhanced DeepONet for Modeling Partial Differential Operators Considering Multiple Input Functions](https://mlsanity.com/paper/2202.08942/) (2022)

## Built on by (most cited first, 30 of 46)

- [UPS: Efficiently Building Foundation Models for PDE Solving via Cross-Modal Adaptation](https://mlsanity.com/paper/2403.07187/) (2024)
- [FlowBench: A Large Scale Benchmark for Flow Simulation over Complex Geometries](https://mlsanity.com/paper/2409.18032/) (2024)
- [RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data](https://mlsanity.com/paper/2601.01829/) (2026)
- [MORPH: PDE Foundation Models with Arbitrary Data Modality](https://mlsanity.com/paper/2509.21670/) (2025)
- [Deep Operator Learning for High-Fidelity Fluid Flow Field Reconstruction from Sparse Sensor Measurements](https://mlsanity.com/paper/2412.08009/) (2024)
- [AMR-Transformer: Enabling Efficient Long-range Interaction for Complex Neural Fluid Simulation](https://mlsanity.com/paper/2503.10257/) (2025)
- [PDEAgent-Bench: A Multi-Metric, Multi-Library Benchmark for PDE Solver Generation](https://mlsanity.com/paper/2605.09636/) (2026)
- [MDBench: Benchmarking Data-Driven Methods for Model Discovery](https://mlsanity.com/paper/2509.20529/) (2025)
- [Information Shapes Koopman Representation](https://mlsanity.com/paper/2510.13025/) (2025)
- [Geometry Matters: Benchmarking Scientific ML Approaches for Flow Prediction around Complex Geometries](https://mlsanity.com/paper/2501.01453/) (2024)
- [AI Benchmark Democratization and Carpentry](https://mlsanity.com/paper/2512.11588/) (2025)
- [NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2602.22059/) (2026)
- [Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems](https://mlsanity.com/paper/2509.20191/) (2025)
- [An MLCommons Scientific Benchmarks Ontology](https://mlsanity.com/paper/2511.05614/) (2025)
- [SynthPix: A lightspeed PIV image generator](https://mlsanity.com/paper/2512.09664/) (2025)
- [Ambient Physics: Training Neural PDE Solvers with Partial Observations](https://mlsanity.com/paper/2602.13873/) (2026)
- [A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modeling](https://mlsanity.com/paper/2606.24696/) (2026)
- [A Comparison of Parametric Dynamic Mode Decomposition Algorithms for Thermal-Hydraulics Applications](https://mlsanity.com/paper/2503.24205/) (2025)
- [Learning Transient Convective Heat Transfer with Geometry Aware World Models](https://mlsanity.com/paper/2601.22086/) (2026)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [Do Physics Foundation Models Learn Generalizable Physics? A Bias-Aware Benchmark Across Physical Regimes and Distribution Shifts](https://mlsanity.com/paper/2605.29283/) (2026)
- [TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learning](https://mlsanity.com/paper/2608.04222/) (2026)
- [Response Renormalization for Critical Deep Equilibrium Models](https://mlsanity.com/paper/2608.23725/) (2026)
- [Benchmarking machine learning models for predicting aerofoil performance](https://mlsanity.com/paper/2504.15993/) (2025)
- [LaPON: A Lagrange's-mean-value-theorem-inspired operator network for solving PDEs and its application on NSE](https://mlsanity.com/paper/2505.12360/) (2025)
- [Improving Large Vision-Language Models' Understanding for Flow Field Data](https://mlsanity.com/paper/2507.18311/) (2025)
- [ChannelFlow-Tools: A Configuration-Driven Pipeline for Generating Machine-Learning-Ready Datasets of 3D Obstructed Channel Flows](https://mlsanity.com/paper/2509.15236/) (2025)
- [UniFluids: Unified Neural Operator Learning with Conditional Flow-matching](https://mlsanity.com/paper/2603.22309/) (2026)
- [FlowForge: A Staged Local Rollout Engine for Flow-Field Prediction](https://mlsanity.com/paper/2604.18953/) (2026)
- [CarCrashNet: A Large-Scale Dataset and Hierarchical Neural Solver for Data-Driven Structural Crash Simulation](https://mlsanity.com/paper/2605.07098/) (2026)

## Abstract (arXiv)

In recent years, applying deep learning to solve physics problems has attracted much attention. Data-driven deep learning methods produce fast numerical operators that can learn approximate solutions to the whole system of partial differential equations (i.e., surrogate modeling). Although these neural networks may have lower accuracy than traditional numerical methods, they, once trained, are orders of magnitude faster at inference. Hence, one crucial feature is that these operators can generalize to unseen PDE parameters without expensive re-training.In this paper, we construct CFDBench, a benchmark tailored for evaluating the generalization ability of neural operators after training in computational fluid dynamics (CFD) problems. It features four classic CFD problems: lid-driven cavity flow, laminar boundary layer flow in circular tubes, dam flows through the steps, and periodic Karman vortex street. The data contains a total of 302K frames of velocity and pressure fields, involving 739 cases with different operating condition parameters, generated with numerical methods. We evaluate the effectiveness of popular neural operators including feed-forward networks, DeepONet, FNO, U-Net, etc. on CFDBnech by predicting flows with non-periodic boundary conditions, fluid properties, and flow domain shapes that are not seen during training. Appropriate modifications were made to apply popular deep neural networks to CFDBench and enable the accommodation of more changing inputs. Empirical results on CFDBench show many baseline models have errors as high as 300% in some problems, and severe error accumulation when performing autoregressive inference. CFDBench facilitates a more comprehensive comparison between different neural operators for CFD compared to existing benchmarks.